No, this is the reference for today's feast, The Birth of St John the Baptist.

This new one for SS Peter & Paul is a bit of a mystery. The Missal asserts no biblical reference for the text at all, not even a "cf. ...". In fact, the second half has an allusion to Matthew 20:22-23: '"Are you able to drink the cup that I am about to drink?" They said to him, "We are able". He said to them, "You will indeed drink my cup..."' The phrase in the first half, 'living in the flesh', reminds me of a bit of an epistle where Paul talks about meeting the Lord 'whether in the flesh or out of flesh, I know not - God knows'. Someone can enlighten me where to find that...

There is no scripture reference in my missal for the Vigil Entrance Antiphon either: "Peter the Apostle, and Paul the teacher of the Gentiles, these have taught us your law, O Lord. " Contextually, both seem to have been written after the death of Peter and Paul, so I'm left wondering whether they could be taken from an ancient text, but not directly from Scripture, despite the scriptural allusions? It's not possible they could be modern, is it?

Definitely an old text. Here's a 14th century chant manuscript. (Click on the little arrow near the top if the side bar is in the way.) These are the ones who, living in the flesh is Isti sunt qui viventes in carne, starting at the big red capital I in the fourth line.

I think the text might be from the Common of Apostles, which (if I read right) was in liturgical books in past centuries but disappeared once each of the apostles had their own propers. There are musical settings, including a couple by Peter Philips from the early 17th century, and this one on cpdl.